For evaluating or designing eyeglass lenses, various evaluation methods and designing methods are proposed to obtain the optimal visibility, and especially a technique is proposed which is focusing on eyesight in a state in which glass lenses are worn. It is referenced, for example, in patent document 1 (Japanese Published Examined Application No. HEI02-39767B (Japanese Patent Provisional Publication No. SHO57-10113A)), patent document 2 (Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2008-511033A), and patent document 3 (Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2000-506628A), that how it can be seen by left and right eyes when a pair of eyeglasses are worn. Further, as references, in patent document 4 (Japanese Patent Provisional Publication No. HEI01-221722A), non-patent document 9 (Bernard et al. Traps in displaying optical performances of a progressive-addition lens,” APPLIED OPTIC, Vol. 31, No. 19, (1992), p. 3586-3593), and non-patent document 10 (“Handbook of Visual Information Processing”, Edited by The Vision Society of Japan, Asakura Publishing Co., Ltd. (2000), p. 285, FIG. 7.1), there is no reference regarding a binocular vision, however, concrete examples of an optical system which represents a positional relationship among an object, an eyeglass lens, and an eyeball are described.
Firstly, examples in patent documents 1-3, that refer to improvements of binocular vision by eyeglasses, are mentioned in order to clarify problems.
The invention described in patent document 1 is a breakthrough patent as an approach to a binocular function. The patent document 1 describes a desired condition in which the binocular function is realized. Namely, a range of an astigmatism in a progressive band, an arrangement of the astigmatism and an alignment error in a whole of a lens, prism ranges of left and right eyeglass lenses, and a condition on directions of skews induced by the prisms are described. However, re-evaluating from the present, the invention described in patent document 1 includes some serious defects.
Firstly, an aberration calculation of a line of fixation emitted from a lens is performed without considering the Listing's law at one eye, which is a primary movement of the eyeball. In this case, the calculation of a residual astigmatism becomes uncertain, and it cannot say that there is the predetermined effect described in the document. Further, the movement of an eyeball of one eye can be considered as a rotational movement performed while centered at one point in the eyeball, that is, the center of the rotation. A frontal plane including the center of rotation at a position from where the eyeball is gazing front is called a Listing's surface. It is the law of major movements of an eyeball that the rotational axis of the eyeball lies within a Listing's surface, and it is called the Listing's law.
Secondly, it is written that progressive portions of the left and right lenses are within the predetermined prism ranges, and that almost the same astigmatisms and alignment errors are taken and defocuses are the same, therefore a stereoscopic vision (it appears that it is a binocular vision) is fine. However, in patent document 1, it is not shown that what balance of the astigmatisms and the alignment errors is fine for the stereoscopic vision, and the extent of fineness is not quantitatively shown. In this regard, it is not clear how the eyeglass lenses described in patent document 1 are configured.
Thirdly, on page 5, lines 25-44 of patent document 1, the explanation of “FIG. 2” of the document is not for an optical system for a binocular vision. This figure is shown in FIG. 22. In FIG. 22, when eyeballs 57 and 58 look straight at a point PP on a subject surface 59, lines of sights 50 and 51 are directed to the point PP. Eyeglass lenses 52 and 53 are arranged in front of the eyeballs 57 and 58. By the prism effect of the eyeglass lenses 52 and 53, for a left eye 57, it is seen that the point PP is placed at an intersection point PL of the line of sight 54 and the surface 59, and, for a right eye 58, it is seen that the point PP is placed at an intersection point PR. It is described in lines 41-42 on the same page that the relationship between the lines of sights shown in FIG. 22 can be deemed as one eyeglass lens which is symmetrical with respect to a prime meridian. However, as it can be seen from Prentice's formula, (P=(h×D)/10), a prism effect is proportional to a dioptric power. Therefore, this assertion is valid only for lenses such that the left lens and the right lens are identical.
Additionally, Prentice's formula is an approximation formula which is sufficient for ordinary use, and it means that prism P of a lens is proportional to a distance, h (in unit of mm), from the center and a diopter D. In short, since optical powers of a left lens and a right lens are generally different, the above described assertion is not obvious, and not established. Further, after the explanation of “FIG. 2” in patent document 1, the explanations are based on one of the left lens and the right lens throughout the document, without specifying a coordinate system and the origin that specify the target point PP. Therefore, the configuration is not suitable for an optical system for a binocular function.
Fourth, the extent of the distortion shown in “FIG. 4” of patent document 1 is difficult to understand. This figure is shown in FIG. 23. The explanation of the figure in patent document 1 exists in line 17 on right column on page 5, where it is explained that the figure is an imaging figure of an equidistant and symmetrical lattice. FIG. 23 is a figure in which positional differences in horizontal direction are drawn from the point PP, when a grid point of the lattice in the surface is set to the point PP. Especially, it can be seen that it is distorted at the lower peripheral part. In lines 25-27 on the same column of patent document 1, it is explained that this is a saddle-shaped distortion or a barrel distortion. Namely, in patent document 1, it is taught that there is a relationship between the positional differences in horizontal direction, ΔPH, and the distortion. When it is assumed that there is a relationship between the positional differences in horizontal direction, ΔPH, and the distortion, the lattice is distorted when all the lines of sights 54 and 55 have intersection points other than the point PP on the surface 59. However, in this case, since the positional differences in horizontal direction are 0, a contradiction arises in that FIG. 23 becomes a figure which is not distorted. Therefore, the positional differences in horizontal direction, ΔPH, has no relationship with the distortion. Further, it is described that a distorted figure is processed as an image drawn with straight lines by a brain. However, a basis is not described regarding, to what extent the figure is distorted, the figure can be processed as lines, though it is an important matter. Therefore, it cannot be clearly understood whether the distortion shown in FIG. 23 becomes straight lines in a brain or not.
Fifth is that the target is on the surface. Basically, the target is arbitrarily determined by a designer. Therefore, in general, eyeglass lenses are designed so that performance of the eyeglass lenses becomes higher at an arbitrarily target determined by a designer. However, in patent document 1, the evaluation method is limited to candidates of the target which are adopted for eyeglass lenses for reading characters on a tight news paper or on a wall. Points within the target other than a fixation point in patent document 1 have big differences in distances from both of the eyeballs. Therefore, it becomes difficult to simultaneously adjust an error in power from the fixation point, a residual astigmatism, and prism. Consequently, the prism becomes bigger. Therefore, in a system in which the target is on a surface, it is difficult to evaluate a binocular vision.
In patent document 2, a design method for eyeglass lenses is proposed. In the design method, a state, in which a front view direction of a person wearing a pair of eyeglasses is shifted toward a side of a dominant eye, is considered. If the shift described in patent document 2 is true for a near vision, then it is an interesting phenomenon and, naturally, there should be an invention which utilizes the physiological phenomenon. However, patent document 2 includes the problems described below.
Firstly, an object to be measured is a living body. Thus, there is a problem on accuracy of measurement. In the example described in paragraph 0030 of patent document 2, it is written that the shift is 2 cm. If it is 2 cm, it is easy to measure, but if the shift is smaller, it becomes difficult to stably measure. It is described in paragraph 0063 of patent document 2 that it can be measured with “an absolute error of less than or equal to 3 mm.” However, taking into consideration that an ordinary amount of an inset for near vision in a progressive power lens is 2.5 mm, the amount of the error is very large.
The second problem is that a phenomenon that “a front view direction is shifted toward a side of a dominant eye” contradicts Hering's law of equal innervations, which is the only one law regarding binocular eye movements. It is difficult to improve a binocular function by designing eyeglass lenses through a measure which is based on a phenomenon contradicting Hering's law of equal innervations. Here, an explanation of Hering's law of equal innervations can be seen in non-patent document 8 (written by Ryoji Osaka, Sachio Nakamizo, and Kazuo Koga, “Binocular Movement and Hering Theory, Experimental Psychology of eye movement”, The University of Nagoya Press, (1993), Chapter 3, p. 60-61, written by Sachio Nakamizo). Hering's theory regarding binocular movement consists of a hypothesis that an innervation of version (ipsilateral binocular movement), which generates binocular movement, and an innervation of vergence (contralateral binocular movement) exist, a hypothesis of equal innervations of both eyes that means amounts of innervations assigned to respective eyes are always equal (Hering's law), and a hypothesis of additivity of innervations that means additivity holds between these two types of innervations.
Further, as a different opinion, it is known that a center of rotation is not fixed and it moves as well as shifts, during ocular movement. It is written, for example, in Japanese Published Examined Application No. SHO 42-9416B (on page 4, right column, lines 16-21) that the center of rotation is such that it does not rotate while centered by a single point and it rotates while centered by different points depending on its use. The assertion of “shift of the front view direction” in patent document 2 can be explained from the fact that a center of rotation of an eyeball itself shifts. Namely, when it is considered that centers of rotation move, a midpoint between the centers of rotation of left and right eyeballs also moves, and a front view direction also moves. In this manner, it is considered that an assumption that left and right eyeballs symmetrically move better conforms to the physiological fact than the assumption that left and right eyeballs asymmetrically move, which is insisted by patent document 2.
Thirdly, it is written in paragraph 0039 of patent document 2 that “a superior binocular fusion is brought.” However, the extent is not clear. Specifically, it is written that if an occurred astigmatism (it is considered a residual astigmatism) is less than or equal to 0.5 diopter, then it is a comfortable field of vision. However, an error in power occurs depending on a target distance. Therefore, a comfortable field of vision is not realized, except for the case in which it is supposed that the target is placed at a position at which the error in power is 0. In an embodiment of patent document 2, two figures, which are a figure of errors in power and a figure of occurred astigmatisms, are shown, depending on conditions of observations. However, their balance are not mentioned. Therefore, it can be hardly understood whether comfortable fields of vision can be obtained, without showing the balance or relationship between an error in power and an occurred astigmatism.
Further, it is incorrect to insist that “a binocular fusion becomes better” by diagrammatically showing only errors in power and occurred astigmatisms. A disorder in which a binocular vision is disabled even if left and right eyes are gaining good abilities to see can be found mainly in many squint patients. In a conventional evaluation of an error in power and an astigmatism such as the evaluation in this patent document 2, the evaluation of performances specific to a binocular vision is not suitable.
Fourth, as in the case of patent document 1, the object of this patent is a surface, as it is apparent from “FIG. 1” or “FIG. 4” of patent document 2. Namely, things that are similar to the fourth indication regarding patent document 1 can be said.
In patent document 3, a technique regarding an eyeglass lens of so-called a wrap-around type, the lens being curved from its front towards an ear side, is disclosed. Further, on page 13 or page 15 of patent document 3, there are some descriptions about off-axis prismatic disparity. Here, defects regarding a binocular vision, the binocular vision being the thesis in patent document 3, are mainly described.
Firstly, it is written that techniques disclosed in patent document 3 are a technique about an eyeglass lens of a wrap-around type or an eyeglass lens of a protective eyewear. However, their configurations are unclear. In the main invention described in patent document 3, it is assumed that there are a prescribed area and a peripheral temporal area. The difference between these two areas lies in shapes of surfaces, as described in pages 28-30 of patent document 3. Here, a method of explaining the difference is not based on evaluation by ray tracing calculations which are commonly used at present, but it is a simplified method which calculates from a shape of a lens surface which has been used for the explanation of a progressive lens in the past. Therefore, the refractive power and the astigmatism are derived values of a curve which are calculated from derivatives of the surface. Thus they are different from those calculated by ray tracing. Further, similarly, there is no description regarding consideration of the Listing's law of movement of an eyeball, which is usually taken into consideration for designing at present. Therefore, it is different from an evaluation or a design which is based on a physiological basis, such as the Listing's law. Further, the peripheral temporal area is so arbitrarily that the difference from the prescribed area becomes not clear. Thus the peripheral temporal area is not forming a limiting condition. Therefore, it can be considered that the description is only valid for normal design of a lens.
Secondly, regarding the definition of off-axis prismatic disparity described in a lower part of page 13 of patent document 3, it is only described that “a defect on a binocular vision arises when an astigmatism at a temporal part and an astigmatism at a nasal part are not equal.” However, the description is insufficient and it cannot be understood what astigmatisms are referred to. Further, as a method of correcting the off-axis prismatic disparity, there is only a description on page 15 of patent document 3 that an aspheric surface is adopted. Thus, the description is insufficient. In addition, though it is clear that the evaluation is performed with a single eye lens, it is concluded on page 13 of patent document 3 that “there is a defect on a binocular vision.” The ground of the conclusion is not clear.
Thirdly, on page 15 of patent document 3, an adjustment among a refractive power, an astigmatism, and a disparity of a prism, and a balance of elements for an optical correction are mentioned. However, the description that a defect on a binocular vision is acceptable as long as the defect is within a range of the values of the table on page 15 cannot be understood. It can be read from this table that a correction amount decreases as a prescribed lens power becomes stronger. It can be read that, “an error is sufficiently corrected with a smaller correction and the defect on the binocular vision is acceptable,” mean that when the prescribed lens power becomes stronger, a patient's tolerance on a binocular vision becomes greater. This assertion is difficult to understand, since it is a description of a tolerance based on single eye evaluation. With the subject matter of patent document 3, in which even a determination method of a tolerance of a binocular vision is not disclosed, it is hard to predict whether it is possible to design so that a tolerance becomes less than or equal to this tolerance, as with a normal standard for eyeglass lenses. Namely, with a description of such a tolerance in a state in which even a binocular vision is not defined, it is not easy to apply this tolerance to a lens design of another general prescription.
Here, it seems that the evaluation of a binocular vision through the single eye evaluation is based on a reason that a temporal portion and a nasal portion must be equal, since, when looking right, a right temporal portion is used in a right lens and a nasal portion is used in a left lens. However, this is a case where there is a precondition that a left lens and a right lens are the same, for example, as addressed in third problem of patent document 1. Such a prescription is very rare. Further, suppose a case in which it is asserted that prescriptions for a left eye and a right eye are almost the same. In this case, taking into consideration that the sensitivity limit in angle of sensory fusion is about 10 seconds in angle, it is difficult to capture a binocular vision with such a rough concept. Moreover, when applying to general-purpose lenses, it is problematic to apply the evaluation and the design that are based on such a tolerance, which lacks a physiological basis, to a human body, even if left and right prescriptions are not known in advance. As a result, there is a risk that it gives discomfort or it increases tiredness.
Next, it is considered that if it is possible to construct an Object-Eyeglass Lenses-Binocular Eyeball Optical System by extending a conventional Object-Eyeglass Lens-Single Eye Eyeball Optical System. FIG. 5 of non-patent document 9 shows a typical Object-Eyeglass Lens-Single Eye Eyeball Optical System. As shown in FIG. 24, a coordinate system of an optical system shown in FIG. 5 shows a center of eyeball rotation as the origin, and an azimuth angle α and an elevation angle β of a viewing angle as respective coordinate values. Additionally, a distance from the center of eyeball rotation to a lens is denoted by q′. Such an Object-Eyeglass Lens-Single Eye Eyeball Optical System as shown in FIG. 24 has been continuously adopted (here a viewing angle has been that of one variable), from the era of Tscherning, that is more than 100 years ago. In this system, the origin of the coordinate is placed at the center of eyeball rotation, since the eyeball rotates. A design reference point is placed at a lens geometrical center, that is a reference point of an aberration. The aberration is represented by differences in optical values along a line of fixation which extends from the center of eyeball rotation to an object through a lens reference point, while setting the design reference point as a reference point. Further, for a case of distant vision, it is common that an object is not shown, since the object is located at a distance of infinity. In order to extend this optical system to a system for a binocular vision, the origin must correspond to two centers of eyeball rotations. Therefore, some ingenuities are required.
Next, an object is considered, when the object is subjected to near vision of the Object-Eyeglass Lens-Single Eye Eyeball Optical System. In this case, technically, a near vision lens can be considered as an eyeglass lens. However, as a matter of fact, the lens is substituted by a far vision lens. Thus, “FIG. 2” of patent document 4, which shows an optical system with a progressive lens, is considered. This figure is shown in FIG. 25. In FIG. 25, a far-point sphere T of a line of sight 1 when viewing far from a center of rotation CR of an eyeball O and states of far view (∞) and near view (0.5 m=2 Dptr) through a progressive lens L are shown. The “object” in this figure is dedicated for the progressive lens and it is one of few examples which diagrammatically shows an object for near view. As shown in FIG. 25, an object at infinity is illustrated in the portion of far view. Conventionally, in the eyeglass industry, an object has been customary denoted with diopter notation. By denoting with diopter notation, as with this example, an infinite distance becomes visible. However, for an evaluation of lens performance, it is not necessary that the object is treated in this way, even if the lens is a progressive lens. Here, it is imagined that it has been arranged only for a target value of an optimization calculation. The subject matter of the invention described in patent document 4 is only for a single eye lens throughout the document, and there is no reference for a binocular vision. Therefore, it is unclear how the object becomes, when the optical system shown in FIG. 25 is extended for a binocular one.
It is considered that, including in the above described patent documents and non-patent documents, there is no Object-Eyeglass Lenses-Binocular Eyeball System, which is commonly used in the eyeglass lens industry, at a time when the present application is filed. Therefore, a configuration of a binocular vision, which can be commonly found in psychology, etc., is considered. There is no configuration of a binocular vision in which a pair of eyeglass lenses are worn. However, there is an Object-Binocular Eyeball System. For example, a Vieth-Muller circle or an iso-convergence circle described on page 39 of non-patent document 3 (Howard, I. P. and Rogers, B. J. “Binocular vision and stereopsis”, Chapter 2, New York, Oxford Press (1995) p. 1-736) or on page 285 of non-patent document 10, etc., can be considered.
FIG. 26 is a diagram showing the Vieth-Muller circle, CV, and the iso-convergence circle, CC, described in non-patent document 10. The Vieth-Muller circle, CV, is defined to be a circle which passes through nodal points nL and nR of left and right eyeballs, and a point F, when both the left eye Le and the right eye Re are fixating the point F. Further, the iso-convergence circle CC is defined to be a circle which passes through centers of rotations CL and CR of both eyeballs Le and Re, and a fixation point F. In FIG. 26, a middle point and a median plane of the centers of the both eyeballs CL and CR are denoted by a point M and a broken line PM, respectively. As it is clear from FIG. 26, the Vieth-Muller circle, CV, is a geometrical horopter (a set of points of outside objects which stimulate corresponding points on retinas of the both eyes; objects on a horopter do not generate retinal image differences) represented by the circle connecting the fixation point F of an object to be seen and the nodal points nL, and nR of the both eyeballs. However, on this Vieth-Muller circle, CV, when a pair of eyeglass lenses are worn, it does not become iso-convergence and, further, it does not have a characteristic such that it is equidistance from a self. Therefore, it cannot be evaluated in an eyeglass lens design. However, according to the Wells-Hering's laws of visual direction, there is an advantage that it is recognized that the origin is on the Vieth-Muller circle and that points on the Vieth-Muller circle are placed at almost equidistance from the self. The iso-convergence circle CC which is resembled to the Vieth-Muller circle CV, namely one in which the nodal points on the Vieth-Muller circle are replaced with the centers of rotations of the eyeballs, is a circle which passes through the centers of rotations of the both eyeballs, and remaining portions are the same as the Vieth-Muller circle. Here, the Wells-Hering's laws of visual direction are laws regarding a question that “why the world seen is one, though it is looked through two eyes.” The Wells-Hering's laws of visual direction are not the laws that directly answer this question, but they are known as the laws which define in what visual direction, the world is seen. Regarding these laws, points (a) and (b) below are known.
(a) An origin of a visual direction is at an eye of Cyclops, which is assumed to be at a middle point of both eyes.
(b) An object on an axis of vision can be seen on a line (a directional axis) connecting an intersection point of both eye axes and the eye of Cyclops.
For example, on page 56 of non-patent document 3, there is an empirical horopter. The figure is shown in FIG. 27. In FIG. 27, an empirical horizontal horopter HL and an empirical vertical horopter HV are ones in which distances, which can be psychologically seen as being equidistance form a self, are traced. The empirical vertical horopter HV has a characteristic such that it is inclined by 2-5 degrees from the vertical direction Vt toward the back side (a side separated from the eyeballs Le and Re). This confirms an experimental fact that it is easy to read, if it is tilted by about 10 degrees, during reading. Since an individual variation is large, it should be adopted as an individual element. However, it is difficult adopt, since actual measured values are few. Further, a range which can be seen to be equidistance is only a cylindrical portion in the figure and there is no other portion. Thus, it cannot be used as an eyeglass system.
As described above, conventionally, “Object-Eyeglass Lenses-Binocular Eyeball System,” which locates an object of both eyes, a pair of eyeglass lenses, and both eyeballs, has not been clearly defined. In the field of psychology, there is a theory in which a neighborhood of a middle point of apexes of corneas of both eyeballs is taken as an origin of a visual direction. However, if that point is set as the origin, then the point moves when the eyeballs rotate up and down, and a conformity with a conventional Object-Lens-Single Eyeball System will be lost. It can be considered that a point on a middle line such that a distance between a fixation point and a center of rotation of one eyeball is equal to a distance between the fixation point and a center of rotation of the other eyeball is taken as the origin of the visual direction. However, it is problematic based on a similar reason. Conventionally, there are some cases in which it is tried to improve a binocular vision by processing of prism effects of eyeglass lenses. However, a realization of an evaluation method of a performance of a binocular vision, the evaluation method being based more on physiological knowledge, is desired.
Based on the above, it is an objective of the present invention to solve the problems described below.
1. To define an origin of a visual direction and a coordinate system that are suitable for an evaluation of a performance of a binocular vision, when a pair of eyeglass is worn.
2. To clarify an “object” which is closely related with an evaluation of a performance of a binocular vision.
3. To perform a quantitative evaluation of a performance of a binocular vision, which is based on a known physiological knowledge on a binocular function, the evaluation being valid in whole surface of a binocular field of view, and the evaluation not depending on a shape of an object.